A. Field of the Invention
The present invention relates to mirrors, and more particularly to substrates or underlying supporting structures for large reflective mirrros for astronomical telescopes.
B. Description of the Prior Art
An astronomical telescope mirror is basically a specular, reflective surface whose geometrical form is maintained by an underlying supporting structure or substrate. Traditionally, an astronomical mirror, large or small, is designed as a cylindrical disc having a diameter to thickness ratio of 8 to 1 (small aperture) or 6 to 1 (large aperture). The smaller ratio, recommended for large mirrors, reflects the importance of self-weight deflection, which is proportional to (Radius).sup.4 /(Thickness).sup.2 for a mirror uniformly supported at its periphery. The long established use of the cylindrical disc as substrate for small aperture has led, by extension, to the use of such cylindrical solid substrates even for large aperture elements. For instance, the ground-based reflection telescope of Kitt Peak is 156 inches in diameter and 26 inches thick. This is characterized by a traditional aperture to thickness ratio of 6 to 1. A disc such as this has to be supported at many discrete points by carefully calculated and controlled forces, arranged to balance the gravitational forces which tend to deform the substrate as the mirror is maneuvered to occupy desired positions.
Thus, it is apparent that with ground based mirrors, as the size increases, the (Radius).sup.4 /(Thickness).sup.2 relation for constant stiffness leads to excessive substrate weight with attendant problems of the support design. The Orbiting Astronomical Observatory (OAO) Program being carried out by NASA has aroused considerable interest in space telescopes. With space-borne telescopes, the reduction of substrate weight becomes even more important. Questions such as total mass to be accelerated in space and changes in the substrate shape as the telescope is taken from the one-g field to zero-g field have to be considered. One promising solution to the two major problems mentioned above is to design substrates having the highest possible stiffness-to-weight ratio.
The self-weight problem associated with large mirrors has long been recognized. The solid disc is not an optimum structure since material near the middle plane, when its axis coincides with the direction of gravity, is not fully stressed. Hence, it is attractive to develop, for both ground and space applications, structural forms in which such understressed material has been redistributed or removed to more effective locations.
Light-weight mirrors have been designed and constructed for satellite and ground applications by the adoption of ribbed and sandwiched structures. In designing mirror substrates, very few designers have made use of the obvious and logical account of certain fundamental theorems touching optimum structural design as enunciated in 1869 by James Clark Maxwell. Maxwell's theorem, shows that one class of optimum structure is that in which all the material employed is stressed, to an acceptable limit, in the same sense; either compression or tension. Membranes, arches and shells have this general characteristic. No examples of the use of arch-like mirror structures have been found in the literature, although suitable forms may be noted from architecture and civil engineering applications. Application of these forms to mirror structures has been getting some preliminary investigation and there has been some indication that these structures would be superior as mirror substrates.
Therefore, it is an objective of the present invention to provide arch type structures for large reflective mirror which have much smaller weight than conventional disc mirrors.
It is a further objective of the present invention to provide arch type structures for large reflective mirrors which are superior to disc mirrors with reference to stiffness.
It is yet another objective of the present invention to provide the above attributes in arch type structures for large reflective mirrors which are easier and more economical to fabricate.
Other objects and many of the attendant advantages of this invetion will be readily appreciated as they become better understood by reference to the following detailed description when considered in connection with the accompanying drawings.